Focus J: Using the Laws of Logarithms
Test yourself (solution)
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Note you may leave the solution in exponential form when
the exponent is large as in this problem.
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An interesting thing happens if we substitute these values
back into the original equation to determine if the solutions are correct.
The x = 5 works fine. However,
when x = -2 is substituted in
and you check it on you calculator you will find that
will
display an error. This occurs because, if you recall, a logarithmic
function is the inverse of the exponential function. If you check its
graph you will see that the argument is always positive. You cannot take
the logarithm of a negative number. Therefore, the root x
= -2 is called an extraneous root
for this equation and the only root is x = 5
.
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